Fire Detection Algorithms Using Multimodal ... - Bilkent University

CHAPTER 6. WILDFIRE DETECTION 100Universal Predictor(x,n)for i = 1 to M dow i (0) = 1 , InitializationMend forŷ u (x, n) = ∑ i v i(n)D i (x, n)if ŷ u (x, n) ≥ 0 thenreturn 1elsereturn -1end iffor i = 1 to M dov i (n + 1) =exp(− 1 2c l(y(x,n),D i(x,n)))∑j exp(− 1 2c l(y(x,n),D j(x,n)))l(y(x, n), D i (x, n)) = [y(x, n) − D i (x, n)] 2end forFigure 6.6: The pseudo-code for the universal predictoralgorithms are linearly combined similar to Eq. 6.9 as follows:ŷ u (x, n) = ∑ iv i (n)D i (x, n) (6.37)where the weights, v i (n), are updated according to the ULP algorithm, whichassumes that the data (or confidence values D i (x, n), in our case) is governed bysome unknown probabilistic model P [74]. The objective of a universal predictor isto minimize the expected cumulative loss. An explicit description of the weights,v i (n), of the ULP algorithm is given as follows:v i (n + 1) =exp(− 1 2c l(y(x, n), D i(x, n)))∑j exp(− 1 2c l(y(x, n), D j(x, n)))(6.38)where c is a normalization constant and the loss function for the i-th decisionfunction is:l(y(x, n), D i (x, n)) = [y(x, n) − D i (x, n)] 2 (6.39)The constant c is taken as 4 as indicated in [74]. The universal predictor basedalgorithm is summarized in Fig. 6.6.We also implemented the Weighted Majority Algorithm (WMA) as the decisionfusion step [47]. The WMA is summarized in Fig. 6.7 [58]. In WMA,as opposed to our method, individual decision values from sub-algorithms are